Do consumers gamble to convexify?

When consumption goods are indivisible, individuals have to hold enough resources to cross a purchasing threshold. If individuals are liquidity constrained, they are unable to borrow to cross that threshold. Instead, we show that such individuals, even if risk averse, may choose to play gamble through playing lotteries to have a chance of crossing the threshold. One implication of this model is that income effects for individuals who choose to play lotteries are likely to be larger than for the general population. This in turn implies that estimating income effects through the random allocation of lottery winnings is likely to be a biased estimate of income effects of the broader population who chose not to gamble. Using UK data on lottery wins, other windfalls and durable good purchases, we show that lottery players display higher income effects than non-players but only amongst those likely to be credit constrained. This is consistent with credit constrained, risk-averse agents gambling in order to cross a purchase threshold and to convexify their budget set.